Exact solution to a Bhatnagar-Gross-Krook-type equation for quantum lattice gases with dephasing noise
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911078895583232 |
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| author | Coppola, Michele |
| author_facet | Coppola, Michele |
| contents | The mean-state dynamics of free fermions subject to random projective measurements of local occupation number operators is governed by a Lindblad equation with dephasing noise. In the continuum limit, the equation of motion for the correlation matrix is mapped to a kinetic equation for the Wigner function, which corresponds to a special case of the Bhatnagar-Gross-Krook (BGK) equation without energy conservation. Our main result is the solution to the kinetic equation, showing that the Wigner dynamics emerges from stochastic sampling of classical run-and-tumble processes. As an application, we recover the crossover between ballistic and diffusive transport regimes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_12155 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exact solution to a Bhatnagar-Gross-Krook-type equation for quantum lattice gases with dephasing noise Coppola, Michele Statistical Mechanics Quantum Gases The mean-state dynamics of free fermions subject to random projective measurements of local occupation number operators is governed by a Lindblad equation with dephasing noise. In the continuum limit, the equation of motion for the correlation matrix is mapped to a kinetic equation for the Wigner function, which corresponds to a special case of the Bhatnagar-Gross-Krook (BGK) equation without energy conservation. Our main result is the solution to the kinetic equation, showing that the Wigner dynamics emerges from stochastic sampling of classical run-and-tumble processes. As an application, we recover the crossover between ballistic and diffusive transport regimes. |
| title | Exact solution to a Bhatnagar-Gross-Krook-type equation for quantum lattice gases with dephasing noise |
| topic | Statistical Mechanics Quantum Gases |
| url | https://arxiv.org/abs/2501.12155 |